So, now there's a new patient on the bench:
For some first tests, I've connected 10V DC / 10V AC to its inputs and found the measured values slowly fluctuating above and below the correct 10.00V reading. All channels voltage and current inputs showed this fluctuation.
OK, time to take it apart, which isn't obvious at the first glance. One has to remove the feet from the bottom (not the back) side, then the whole instrument slides out of its outer cover. Another about ten screws later, one can lift the internal top cover. To the left, three shielded boxes (voltage inputs), below (not visible) another three shielded boxes for the current inputs. Right hand side, the main processing board is buried under the printer drawer and the power supplies. Yes, it's got two of them: One 5V, 12V, -12V, the other 24V for the printer.
First I checked the supply voltages: Look fairly OK, no signs of excessive ripple. Ran the unit off a lab supply just to be sure - no change in the fluctuations.
Next, I had a look at the input modules. Each has two isolated paths: current and voltage, and each has its own isolated supply, powered by some square wave AC through small transformers. So I checked the isolated voltages: One thing is in common - they're all too low. About 9.8V, and fluctuating, where I'd expect 12V, about 4V fluctuating instead of 5V (just an educated guess, don't have a service manual). These are outputs of (apparently) smallish 78L12 style regulators, so I checked their inputs - too low for this kind of regulator.
So far until now, I'll have to come back later to find out how to remove the printer drawer to gain access to the main board and find the source of the square wave AC supplying the input boards. I'd guess there's something bad within this circuit.